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A fast computing decoder for polar codes with a neural network

Lingxia Zhou, Satya Chan, Meixiang Zhang, Sooyoung Kim

Published Feb 16, 2023• 6 citations
Publisher

Abstract

This paper proposes high-speed computing decoders for polar codes based on a neural network. To compensate for the performance gap with the successive cancellation decoder, we propose applying the recurrent neural network to the BP decoder with a modified factor graph to reduce the computational complexity of the decoder without any performance degradation. The results of the performance simulation conducted in this paper reveal that the proposed decoder requires substantially less computational complexity than the conventional decoders to achieve the same bit error rate performance.

DOI
10.1016/j.icte.2023.02.005

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This paper proposes high-speed computing decoders for polar codes based on a neural network. To compensate for the performance gap with the successive cancellation decoder, we propose applying the recurrent neural network to the BP decoder with a modified factor graph to reduce the computational complexity of the decoder without any performance degradation. The results of the performance simulation conducted in this paper reveal that the proposed decoder requires substantially less computational complexity than the conventional decoders to achieve the same bit error rate performance.
Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree.
In recent years, the emerging Deep Learning (DL) technology has made progress in the field of decoding. Current polar code neural network decoder has faster convergence speed and better Bit Error Rate (BER) performance than Belief Propagation (BP) decoding. However, it still has the problem of high computational complexity. Therefore, in order to improve this problem, this paper adopts the idea of improving information update in the iterative process, and proposes a Recurrent Neural Network (RNN) Offset Min-Sum (OMS) BP decoding algorithm that improves Left information update (RNN-OMSBP-L) . The simulation results show that, compared with the Deep Neural Network (DNN) BP(DNN-BP) decoding algorithm, this algorithm replaces all multiplications with a cost of 6.25% addition. Compared with the current optimized RNN OMS and approximate BP(RNN-OMS-BP) decoding algorithm, the decoding algorithm in this paper uses improved information to reduce 25% of the addition operations with almost no loss in BER performance, while saving part of the storage space overhead. Under the same BER performance, it reduces the number of iterations by 37.5%.
The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the art polar decoders such as successive cancellation list and belief propagation decoding.
Polar codes are considered as a competitive candidate for 5G ultra-reliable and low-latency communication (URLLC) channel codes, but its strict latency and reliability requirements pose signicant challenges to the existing decoding schemes, especially in terms of decoding latency. In this paper, we propose a neural network based successive cancellation (NN-SC) decoding algorithm. In the proposed algorithm, neural networks are used to replace the local decoders for rate-R constituent codes because of their one-shot decoding capacity, which greatly reduce the decoding latency and algorithmic complexity. The simulation results indicate that the NN-SC decoding algorithm can achieve comparable reliability performance against the successive cancellation (SC) decoding for a polar code of length 128 and rate 1/6, while reducing the decoding latency by 65.2% when compared with the simplified SC decoding. In addition, for two conventional decoding algorithms: SC and belief propagation (BP) decoding, the proposed algorithm can further reduce the decoding latency by 22.8% and 13.8%, respectively.
With the development of communication technology, it is urgent to design channel decoding algorithms to maximize the high throughput and minimize the latency. As the capacity achieving polar codes are adopted by 5-th generation wireless system (5G), it is required to design efficient the decoding algorithms for polar codes with high performance and low complexity. Deep neural network (DNN)-based algorithms which have shown superiority in other fields, can obtain better performance using multi-scale belief propagation (BP) algorithm, whereas the decoding complexity needs to be decreased. We propose a residual neural network based belief propagation (ResNet- BP) algorithm to solve the inherent drawbacks in the existing methods, by reducing the number of variables in the network and reducing the complexity in terms of multiplication. Simulation results demonstrate that the proposed method can achieve the approximating performance of recurrent neural network-based belief propagation (RNN-BP) with a lower number of iterations.
Abstract Compared with SC decoding, BP decoding with the parallel mechanism has higher throughput and lower latency, which is more suitable for the demand of 5G scene. To further improve its FER performance and reduce the memory overhead, a recurrent neural network-aided bit-flipping BP decoding of polar codes is proposed. Firstly, it uses bit flip to correct the wrong decoded bits during the decoding iteration. And then, the offset min-sum approximation is used to replace multiplication operation. Lastly the improved recurrent neural network architecture is adopted to realize parameter sharing. The simulation shows that the proposed scheme has a better error correction ability with fewer flipping times, and can effectively reduce the computational resource consumption and extra memory overhead of BP decoding.